686 IONIC RADIUS AND IONIC EFFICIENCY 



radius loses its meaning in this case unless we substitute for such 

 polyatomic ions a monatomic model with one nucleus, one ring of 

 valency electrons and a radius calculated in such a way as to render 

 the electrostatic effect of the monatomic model equal to that of the 

 polyatomic ion which it is supposed to represent. 



The rule at which we arrived, namely that the efhciency of the 

 anions increases directly with their ionic radius while the efficiency 

 of the cations increases inversely with their ionic radius, is probably 

 of general applicability in physical chemistry as well as in physiology, 

 wherever the efficiency of ions depends on their electrostatic action. 



There are numerous observations in the physiological literature 

 which indicate an inversion of the order of efficiency of monovalent 

 cations when the reaction of the solution changes from basic to acid. 

 It is possible that these facts will find their explanation on the basis 

 of our rule; namely, that on one side of the neutral (or in certain cases 

 the isoelectric) point the effect observed is increased by the cation 

 and inhibited by the anion, while on the other side it is increased by 

 the anion and inhibited by the cation. Unfortunately the facts given 

 are often too incomplete to test this idea and the experiments are 

 generally done with such high concentrations of electrolytes that it 

 is doubtful whether they can be used for any conclusions concerning 

 the specific effects of ions. 



SUMMARY. 



1. It has been shown in preceding papers that when we separate 

 solutions of electrolytes from pure water by collodion membranes the 

 ions with the same sign of charge as the membrane increase while 

 the ions with the opposite sign of charge diminish the rate of diffusion 

 of water from the side of pure water to the side of solution; and that 

 the accelerating and depressing effects of these ions on the rate of 

 diffusion of water increase with their valency. 



2. It is shown in this paper that aside from the valency a second 

 quantity of the ion plays a role in this effect, namely the radius, 

 which in a monatomic ion means the distance between the central 

 positive nucleus and the outermost ring or shell of electrons of the 

 ion. In monatomic, monovalent anions the radius increases in the 



